Perturbation theory of the Fermi surface in a quantum liquid. A general quasiparticle formalism and one-dimensional systems.

We develop a perturbation theory formalism for the theory of the Fermi surface in a Fermi liquid of particles interacting via a bounded short range repulsive pair potential. The formalism is based on the renormalization group and provides a formal expansion of the large distance Schwinger functions in terms of a family of running couplings consisting of a one and two body quasi particle potentials. The flow of the running couplings is described in terms of a beta function, which is studied to all orders of perturbation theory and shown to obey, in the n–th order, n! bounds.......